{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "mu, sigma = 0, 0.4 # mean and standard deviation\n",
    "x = np.random.normal(mu, sigma, 100000)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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I27OVbQOcD3wh/f41wN4S3udW4jwHuLWM/bAmhtcD48B3Gjxf+rZsMc7St2Ua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\nBCEiIplDI3qQAAAABklEQVT+P+L2dwpxi84AAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107efca90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('p(x)')\n",
    "plt.title('Position')\n",
    "\n",
    "plt.grid(True)\n",
    "count, bins, ignored = plt.hist(x, 500, normed=True)\n",
    "plt.show()\n",
    "#prob_x = 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) );\n",
    "    \n",
    "#plt.plot(bins, prob_y, linewidth=2, color='b')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  0.,  0., ...,  0.,  0.,  1.]),\n",
       " array([-1.07212767, -1.07170104, -1.07127441, ...,  1.0601751 ,\n",
       "         1.06060173,  1.06102836]),\n",
       " <a list of 5000 Patch objects>)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gSyjqLZe/u1me3JRsdTlwnruMTL3lxk24RKaOKvEcnj8ydQAARb1L0iMBR8sulfftN2/T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\nAaBD/h+io3SiX6vrvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1099f8c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_y = np.array(x);\n",
    "for i in range(0,len(x)):\n",
    "    prob_y[i] = np.arctan(x[i])\n",
    "    \n",
    "#prob_y = np.arctan(x)\n",
    "plt.hist(prob_y, 5000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Dr3/t1WAlpZTwY1u5Ek47zbct7NNHsxYkv5xySsXm5wMG+KpySRlNy4xpwwY4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\n5AklfBGRPPH/AWUeEe+Fym9IAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109371650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "mu, sigma = 0, 0.4 # mean and standard deviation\n",
    "x = np.random.normal(mu, sigma, 100000)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
